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Munich Personal RePEc Archive

Peer Group Effects on the Academic

Performance of Italian Students

De Paola, Maria and Scoppa, Vincenzo

Department of Economics and Statistics, University of Calabria

(Italy)

January 2009

Online at

https://mpra.ub.uni-muenchen.de/18428/

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1

Peer Group Effects on the Academic Performance

of Italian Students

Maria De Paola and Vincenzo Scoppa*

Working Paper Version

Forthcoming in Applied Economics, 2010

Abstract. We analyse peer effects among students of a middle-sized Italian public university. We explain students’ average grade in exams passed during their Second Level Degree course on the basis of their pre-determined measures of abilities, personal characteristics and peer group abilities. Thanks to a rich administrative dataset, we are able to build a variety of definitions of peer groups, describing different kinds of students’ interaction, based on classes attended together or exams taken in the same session. Self-selection problems are handled through Two-Stage Least Squares estimations using as an instrument, the exogenous assigning of students to different teaching classes in the compulsory courses attended during their First Level Degree course. We find statistically significant positive peer group effects, which are robust to the different definitions of peer group and to different measures of abilities.

JEL Classification: I21; Z13; J24.

1. Introduction

Educational economists have highlighted, in theoretical and empirical studies, the relevance of

peer group quality to student performance (Epple and Romano, 1998; Hoxby, 2000). A peer

group affects student achievement in several ways: members of a group interact in learning,

help each other in their studies, share important information, impose externalities on others by

behaving well or badly (for example, a noisy student disrupts the study environment) or by

allowing teachers to go deeper in subjects, contribute to the formation of values and aspirations,

and so on.

Understanding the nature and the magnitude of peer group effects in education is crucial

for the “productivity” of educational processes and the organizational design of school systems.

For example, in order to improve student outcomes, it is important to know which inputs

influence their performance most and the relative importance of peer effects compared to other

inputs, such as teacher quality or school resources. Peer effects are also important in school

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design. If peer effects are at work, educational outcomes are affected by how students are

arranged across classes and the desirability of comprehensive schools (which mix students of

different abilities together) or stratified schools (which tend to aggregate students according to

their abilities) depends on the magnitude and non-linearity of peer effects. Further more, the

selectivity of university admission policies produces different results in the presence of peer

effects. More importantly, the nature of peer effects also has fundamental implications in a

family’s choice with regards whether parents consider that their offspring would benefit from

schools which sort students according to their abilities.

Starting from the classical study of Coleman et al. (1966), a host of works have

analysed the effects of peer group on children’s achievement and educational outcomes (Betts

and Morell, 1999; Hoxby, 2000; Angrist and Lang, 2004; Hanushek et al., 2003) and on college

students’ grades and choices of fields of study (Sacerdote, 2001; Zimmerman, 2003; De Giorgi,

Pellizzari and Redaelli, 2006; Foster, 2006), but several problems and controversies are still

unresolved. Some of these studies show that peer effects are statistically and economically

significant in a variety of educational contexts and that students tend to perform better if the

quality of their peer group is higher (Ding and Lehrer, 2006; Zimmerman 2003; Vandenberghe,

2002; Hoxby, 2000; Sacerdote, 2001; Zimmer and Toma, 2000). Moreover, a number of these

studies show that peer effects are often non-linear, implying that students of middle abilities are

particularly affected by the negative influence of weak students (Sacerdote, 2001; Zimmerman,

2003). However, the significance and size of peer effects often changes in relation to the sample

used. Other studies, in fact, find no significant (or minor) peer effects (Angrist and Lang, 2004;

Arcidiacono and Nicholson, 2005; Foster, 2006).

Earlier analyses of peer effects were based on simple econometric models regressing

students outcomes on their own individual characteristics (measures of ability, family

background and so on) and on their peers’ outcomes or characteristics.

As shown by Manski (1993), this kind of regression is plagued by two main

econometric problems, which raise doubts about the causal interpretation of the coefficient

measuring peer group effects. The first problem, known as “self-selection” bias, depends on the

fact that groups of peers are often not exogenously determined, but individuals typically choose

the other people they will associate with . Therefore, the characteristics of each student

contribute to determining the choice of his/her peers and, if some of these characteristics are not

observable, an endogeneity problem arises.

The second econometric problem, known as the “reflection” problem, emerges because

the outcomes of students in a peer group evolve in an interdependent manner: the achievements

of each member affects the achievements of other members but, at the same time, is, itself,

affected by the achievements of those self-same peers. Therefore, an estimation bias emerges,

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Recent empirical studies have undertaken a variety of estimation strategies to handle

these problems. A strategy used by a number of researchers is that of relying on some sort of

natural experiment which brings about random assignment of peers. Sacerdote (2001),

Zimmerman (2003) and Foster (2006) analyse peer group effects among undergraduate students

who are randomly assigned to a college residence. Recently, De Giorgi, Pellizzari and Redaelli

(2006) have used random assignment to teaching classes as identification strategy to estimate

peer effects on the choice of the field of study. Other works rely on instrumental variables to

remove the correlation between unobserved characteristics and peer characteristics trying to find

exogenous determinants of peer quality (Evans, Oates and Schwab, 1992; Case and Katz, 1991).

A number of papers try to take into account the endogeneity of the peer group by controlling for

school and individual fixed effects (Arcidiacono and Nicholson, 2004; Hanushek et al., 2003).

Most of the works on peer effects among college students use data from (highly

selective) US universities, whereas few works have analysed peer effects in European

universities. Our analysis is an attempt to reduce this gap by providing evidence of peer effects

among students of a middle sized Italian university located in the South of the country.

Importantly, while most of the work on peer effects in tertiary education considers residential

peer groups emerging among roommates, we are able to analyze the effects produced on student

performance by interaction among students who share the same teaching environment and study

together.

Thanks to a rich administrative dataset of students enrolled in the Second Level Degree

(“Laurea Specialistica”)1course in Business Administration at the University of Calabria, we are

able to build different definitions of the peer groups, mainly based on students attending classes

together and sitting their exams in the same session. This allows us to investigate peer group

effects which operate among classmates through mechanisms which rely on the fact that

classmates contribute to the shaping of their educational environment and that students typically

interact and establish friendly relationships with students attending lectures in the same classes.

Classmates with high abilities help create a more effective learning process: instructors

are not interrupted by students asking silly questions and are able to use more challenging

material, in addition they are encouraged in their teaching activity by interested and clever

students etc. (see Lazear, 2001). We consider this kind of effect through a measure of a peer

group based on students attending courses together. For each student i we consider, as members

of his/her peer group, those students who have taken courses together with i. Peer group quality

is then calculated as the weighted average of abilities of students in the group, using the number

of courses taken together as weights.

Apart from peer effects related to the classroom environment, students belonging to the

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same class tend to study and revise the subject together, so generating important externalities.

Clearly friendly relationships do not involve all members of a class: some students might attend

a course together, but their interaction might still be limited. We are able to address this

problem by considering a measure of peer group which weights peers in relation to the number

of exams taken together. In fact, students who continually do exams in the same session as one

another are often students who study together, sharing course material and information. We look

at all the students passing an exam on the same date and we use this information to define a

second measure of peer group quality, which weights the abilities of each student according to

the number of exams taken together with student i.2

We are aware that these definitions may be affected by self-selection problems since

students choose other people to collaborate with in studying. In order to overcome possible

self-selection problems, we use a Two-Stage Least Squares estimation and instrument peer groups

through the random (and compulsory) assignment of students to different teaching classes

during their First Level Degree course (for a similar strategy, see Foster, 2006).

Our estimations show that peer group abilities have considerable, positive effects on

students’ academic performance. These effects are not brought about by self-selection and are

robust to a variety of definitions of peer group and several measures of abilities. In our preferred

Instrumental Variable specification, we find that an increase of one standard deviation in peer

group quality (measured as the average ability of students attending the same course) produces

an increase in student performance of 0.19 (the OLS estimates show a smaller effect equal to

0.13). This is quite a large effect, since the effect produced by an increase of one standard

deviation in the student’s own ability generates an increase of 0.54. Effects are slightly higher

when we consider our second measure of peer group quality, based on repeated interaction at

exams, implying that this measure is able to take into account some relevant interaction taking

place among students.

These results suggest that student quality is an important input in tertiary education and

that, in order to improve their students’ performance, colleges and university should attract high

quality students. Our results are consistent with selection policies adopted by many US

universities aimed at admitting only the best students. They also support the idea that students

applying for highly reputable institutions evaluate not only the high quality of instructors

provided, but also the high-quality of peers. Moreover, if student performance is determined, at

least in part, by his/her effort then is rational to subsidize good students for the positive

externalities they produce.

This paper is organized in the following way. In section 2, data are presented and some

descriptive statistics are offered. In section 3, we estimate a simple OLS model. In section 4, we

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instrument our measures of peer group by using the exogenous assignment of students to

different teaching classes as an instrument. Section 5 concludes.

2. Data and Descriptive Statistics

Our analysis is based on administrative data from the University of Calabria, a middle-sized

public university located in the South of Italy. It has currently about 31,000 students enrolled in

different degree courses and at different levels of the Italian University system, which, since the

University Reform of 2001, is organized around two main levels, comprised of First Level

Degrees (3 years legal duration) and Second Level Degrees (2 years). Students who have

acquired a First Level Degree can undertake a Second Level Degree.3 In order to gain a Second

Level Degree students have to pass about 20 exams and to write a dissertation, obtaining a total

of 120 credits.4

We focus our analysis on students enrolled, for the academic years 2004-2005 and

2005-2006, on the Second Level Degree course in “Business Administration” (“Laurea

Specialistica in Economia Aziendale”). The administrative data we have at hand provide

detailed information on students’ personal characteristics, secondary school and academic

results, gender, type of High school attended and final High school grade, province of

residence5, grades obtained on each course and date of each exam, grades obtained in the First

Level Degree course, and initial year of enrolment.6

We started with a sample of 267 students, but we excluded students who had done

fewer than 3 exams and, to render students enrolled in different years comparable, we only

considered exams taken in the first year of their Second Level Degree. Moreover, since, in our

analysis, we use information about the academic career of students who have acquired their

First Level Degree at the University of Calabria, we excluded some observations and our final

sample was composed of 212 students.

Table 1 provides descriptive statistics for the sample of students we use. During the first

year of the Second Level Degree course, our sample of students passed an average of 7.71

exams per student. Grades range from 18 to 30 and “30 cum laude”, which we consider equal to

31. The Average Grade over the exams taken by each student is the measure of academic

performance which we use as a dependent variable. The mean of Average Grade is 27.05 and its

standard deviation is 2.06.

About sixty percent of the students were female. 76 students (36%) were enrolled in

their second year and 136 in their first. Students mainly came from two different types of High

school: Lyceums (about 34%) and Technical and Vocational Schools (about 66%). Final High

3

After Second Level Degree students can enrol in a Ph.D degree.

4

Each course typically gives 5 credits.

5

Provinces correspond to the Nuts 3 Eurostat classification.

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school Grade (which we denote throughout the paper as AbilityHS) ranges from 60 to 100, with

a mean of 89.17. The average grade they obtained at exams during their First Level Degree

(denoted as AbilityFirst) is 25.58. The Final First Degree Grade ranges from 86 to 110 and

“110 cum laude” (which we set as equal to 111) and has a mean of 102.96.7

In order to define a single index of individual ability (denoted as Ability), we undertook

a principal component analysis summarizing the different measures of ability which we had

available (AbilityHS, AbilityFirst, Final First Degree Grade, a dummy for the type of High

School denoted as Lyceum)8. Principal component analysis creates linear combinations of the

original variables which capture the greatest variance. We only use the first principal

[image:7.595.84.507.306.411.2]

component.

Table 1. Descriptive statistics for the sample of students enrolled on the Second Level Degree course in Business Administration

Variables Mean Std. Dev Min. Max. Obs.

Average Grade in exams 27.046 2.062 19.667 30.6 212

Number of exams passed 7.707 2.592 3 13 212

Female 0.618 0.487 0 1 212

Year of enrolment 0.358 0.481 0 1 212

Final First Level Degree Grade 102.962 6.762 86 111 212

Average Grade in First Level exams (AbilityFirst) 25.579 1.710 21.682 29.472 212

High School Final Grade (AbilityHS) 89.171 11.387 60 100 212

High School Type: Lyceum 0.340 0.475 0 1 212

Ability -0.123 1 -2.291 1.915 212

Notes: Grades in each course ranges from 18 to “30 cum laude” (set equal to 31). Final High School Grade ranges from 60 to 100. Final First Level Degree Grade ranges from 66 to “110 cum laude” (set equal to 111).

3. Econometric Estimations of Peer Group Effects

We analyse the influence of peer groups on academic performance assuming that a student’s

academic performance is determined by his/her own characteristics and by the performance and

characteristics of his/her peers (Sacerdote, 2001). Therefore, we start from the following simple

model:

[1] Yi =α+βXiXjYjziji

where Yi is the performance of student i, Xi is a vector of individual characteristics of i

(measures of his/her ability and personal characteristics), Xj includes the (predetermined)

characteristics of j, belonging to the peer group of i (“contextual effects” in the definition of

Manski, 1993) and Yj are the outcome of i’s peer (Manski’s “endogenous effect”), zij are

common (unobservable) characteristics of the peer group including student i (“correlated

effects”), εi is an error term.

7

The Final First Level Degree Grade is calculated on the basis of the average grade obtained at exams. In our regressions, we prefer to use AbilityFirst because the Final Grade compresses variability (typically each student with an average grade of 27.5 or more obtains the maximum final grade, “110 cum laude”).

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As mentioned previously, this model faces two main econometric problems:

“reflection” and “selection” bias. With regards the “reflection” problem, that is the fact that the

achievement of student i, Yi, is determined by the performance of his/her peers, Yj, but,

simultaneously, Yj is determined by Yi, we follow the literature (see Sacerdote, 2001;

Ammermueller and Pischke, 2006), and considering an equation symmetric to [1] for the

performance of each student j in i’s peer group , by substitution, we obtain the following

reduced form equation:

(

)

(

2

)

(

(

2

)

)

(

(

2

)

)

(

)

(

1

(

2

)

)

1 1

1 1

1

γ ε γε ψ γ γ

γβ φ γ

γφ β γ

γ α

− + + +

+ −

+ + −

+ + −

+

= ij j i

j i

i

z X

X Y

or, more simply:

[2] Yi=α~+β~Xi+φ~Xj+ε~

By estimating equation [2], we are therefore unable to recover the structural parameter

φ and γ and distinguish “endogenous” from “contextual” peer effects, but, in equation [2], we

obtain the magnitude of “total peer effects” φ~, which is what matters from a policy point of

view, although it may be unsatisfactory from a theoretical perspective.

Another important problem, which may lead to a biased and inconsistent estimate of φ~

using OLS, is the endogeneity of Xj, due to the fact that individuals typically select people

with whom to associate. This clearly contrasts with an ideal situation in which individuals are

randomly assigned to different peer groups. If peers are selected according to individual

characteristics that affect his/her own level of attainment (but are unobservable to the

researcher), we may end up considering as a peer effect something that, instead, depends on the

individual’s own attributes which are captured through his/her peer group quality.

This issue is particularly relevant for our analysis, since our peer group measures are

based on students taking common courses and exams: students with similar characteristics are

likely to choose the same courses or to sit a particular exam in the same session. We tackle this

problem by using, as an instrumental variable for peer group quality, the random assignment of

students to teaching classes, which, we believe, influences peer group formation, but is not

correlated to the error term ~ , and estimating with the classical Two-Stage Least Squares zij

(Evans, Oates and Schwab, 1992).

We first estimate a single-equation model with Ordinary Least Squares (OLS) assuming

that peer group quality is exogenous. In the next Section, we extend the model to deal with the

endogeneity problem, treating peer group as a choice variable.

Our dependent variable Yi is the Average Grade in exams taken by student i during

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measures are considered of i’s own ability: Final High School Grade (AbilityHS), Average

Grade in the First Level Degree course (AbilityFirst), and a composite index of individual

ability (Ability)). Other personal characteristics included in vector Xi are: a gender dummy

(Female), a dummy for the type of High School (Lyceum), and dummies for province of

residence.

In order to take into account the levels of difficulty of the different courses chosen by

each student (or different evaluation criteria used by different lecturers),9 we control, in each

regression, for the average of the grades (Average Course Grade) obtained by all other students

taking a given exam and consider the average over all of the exams taken by student i. Since, as

we explain below, our sample students have attended part of their First Level Degree courses in

different teaching classes, we control for some quality characteristics of the instructors teaching

in each classes which may affect students’ performance, such as research activity (Instructors’

Publications) and teaching experience (Instructors’ Experience). As these regressors vary at

teaching classes level, in order to avoid biased standard errors, we estimate our models

clustering the standard errors at this level (Moulton, 1990).

All variables have been standardized in order to make results comparable in different

specifications and to render the interpretation of marginal effects more straightforward.

In Table 2, we report estimates of alternative specifications of our model. In all

specifications, standard errors (reported in parentheses) are corrected for heteroskedasticity. All

equations include province of residence dummies (not reported so as to save space).

In column 1, we first estimate an equation without peer effects to check which factors

determine academic performance. We show that AbilityFirst greatly explains our dependent

variable, while AbilityHS is not significant.10 Average Course Grade is positive and highly

significant. The Female and Lyceum dummies are not significant, nor are the dummies for

province of residence. Variables measuring teaching quality on the First Level Degree courses

show a positive and statistically significant effect.

The other columns in Table 2 include peer group quality among explanatory variables.

We use different measures of peer group quality. From a theoretical point of view, it is not clear

whether a student is influenced mainly by his/her close friends, or by his/her classmates, or by

his/her roommates in college, or by people from his/her place of residence. Our definitions of

peer group are at an aggregate level and tend to describe different types of interaction among

students.

Our first definition of peer group (Peer Course) is based on the group of students who

9

Students have a certain freedom to choose courses in their Degree program, after some compulsory courses.

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have taken a given course, attending classes and taking the exam in the same academic year.

Therefore, in this case, we are assuming that the relevant peer group is represented by people

who attend classes together. As shown by Lazear (2001), education in a classroom environment

is almost a public good. Weak students may impose negative externalities on other students by

disturbing or slowing-down learning and viceversa.

Students on the Second Level Degree course in Business and Administration at the

University of Calabria enrol in a wide range of courses. We do not observe directly the

composition of students on each course, but we infer this information from exams taken by

students in a given year.

For each exam k taken by student i, we first determine the average ability (using

different measures: AbilityHS, AbilityFirst and Ability) of all other students taking the same

course. Then, we take the average over all the exams taken by i to calculate the ability of i’s

peer group:

∑ ∑

= = ⎟

⎟ ⎠ ⎞ ⎜

⎜ ⎝ ⎛

= i k

N

k

J

j j k i

i A

J N Course Peer

1 1

1 1

where Aj is the ability of j, Jk is the number of peers in the exam k, Ni are the exams taken by i.

The average number of exams taken by each students is 7.7111, while the average number of

students in each course is 24.82.

Columns 2, 3 and 4 of Table 2 use AbilityHS, AbilityFirst and Ability respectively as a

measure of peer ability Aj. In all specifications, controlling for individual characteristics and

teaching quality, peer effects appear positive and significant. An increase in the

(pre-determined) ability of the peer group of student i (whichever way it is measured) leads to an

improvement in the academic performance of i. For example, as shown in column 4, an increase

in the ability of the peer group (measured as Ability) of one standard deviation leads to an

improvent in student performance of about 0.13. The coefficient is significant at 5 percent

level.

Smaller effects emerge when we measure peer group ability on the basis of final High

School grade or of average grade during the First Level degree course (respectively AbilityHS

and AbilityFirst). As it is possible to see in columns 2 and 3, the coefficient is in, both

cases,about 0.06, significant respectively at 10 and 5 percent level.

The other explanatory variables have approximately the same level of significance as in

column 1. Student’s own abilities, measured by the average grade during the First Level Degree

course (or by Ability), is, in each specification, positive and highly significant. An increase of

one standard deviation of an individual’s own ability improves performance by about 0.55.

Average Course Grade is always significant, implying that courses chosen by students have

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different degrees of difficulty. Our variables explain more than 50% of total variability.

In column 5, we investigate the existence of non-linearity in peer effects. Using Ability,

we have created two dummy variables for whether or not peer group quality was in the top 25

percent (Peer Course Top), or in the middle 50 percent of the distribution (Peer Course

Middle). The bottom 25 percent (Peer Course Bottom) represents the omitted category. As

shown in column 5, students are positively affected by having a peer group of high and medium

quality (statistically significant respectively at 5 and 1 percent level). The magnitude of

coefficients is very similar, implying that having a peer group of medium ability instead of one

of high ability does not produce any relevant change in student performance. Results do not

change when using different measures of ability.

Following Betts and Morell (1999), in column 6, we also verify whether

socio-economic characteristics of the community where students come from influence their

performance. We introduce an indicator of educational level, measured as the percentage of

people living in the area (town or city) where student i is resident with a college or a high

school diploma (Population with College or HS), average income (Income), and the

unemployment rate in the area (Unemployment).12 These socio-economic characteristics do not

seem to play a relevant role in shaping students’ performance, since their coefficients are all not

statistically significant.

12

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[image:12.595.84.509.93.450.2]

11

Table 2. OLS regression estimates for academic achievement.

Dependent variable: Average Grade in Second Level Degree course exams

Explanatory Variables 1 2 3 4 5 6

AbilityFirst 0.565***

[0.062] 0.545*** [0.058] 0.541*** [0.056] 0.539*** [0.069]

AbilityHS 0.074

[0.044] 0.082 [0.047] 0.085 [0.043] 0.092* [0.043]

Ability 0.554***

[0.051]

0.558***

[0.051]

Female 0.004

[0.038] -0.009 [0.043] -0.015 [0.044] -0.117 [0.067] -0.133 [0.101] -0.009 [0.051]

Lyceum -0.003

[0.106] 0.004 [0.103] 0.006 [0.102] 0.001 [0.111]

Average Course Grade 0.357***

[0.027] 0.344*** [0.029] 0.353*** [0.027] 0.326*** [0.027] 0.304*** [0.048] 0.339*** [0.022] Instructors’ Publications 0.326**

[0.099] 0.276** [0.082] 0.233** [0.083] 0.234 [0.119] 0.344* [0.201] 0.226* [0.096] Instructors’ Experience 0.375**

[0.112] 0.310** [0.097] 0.259* [0.102] 0.236 [0.139] 0.363* [0.204] 0.256* [0.102]

Peer Course (AbilityHS) 0.059*

[0.026]

0.064* [0.026]

Peer Course (AbilityFirst) 0.065**

[0.023]

Peer Course (Ability) 0.131**

[0.390]

0.558*** [0.051]

Peer Course Middle 0.347***

[0.132]

Peer Course Top 0.330**

[0.163]

Income -0.028

[0.048]

Population with College or HS -0.001

[0.060]

Unemployment rate -0.079

[0.042]

Constant -0.146

[0.092] -0.146 [0.085] -0.138 [0.091] -0.108 [0.101] -0.412** [0.185] -0.171** [0.057]

Adjusted R2 0.568 0.569 0.569 0.535 0.569

Observations 212 212 212 212 212

Notes: In all regression dummies are included for province of residence. Standard errors, corrected for heteroskedasticity and adjusted for potential clustering at teaching classes level, are reported in brackets. The symbols ***, **, * indicate that coefficients are statistically significant, respectively, at 1, 5, and 10 percent level.

4. Instrumental Variable Estimations

In OLS estimates in Table 2, we assumed that peer group quality is an exogenous variable.

However, individuals typically choose with whom they will associate and so peer quality is, to

some extent, endogenous. In this case, a regression of student performance on peer abilities

would be biased and inconsistent because of an endogeneity problem. Therefore we have to deal

with this problem in order to measure the relevance of peer effects consistently, identifying

cases where the peers were assigned essentially randomly (see Evans, Oates and Schwab, 1992;

Foster, 2006).

We need to find an instrumental variable Z which must comply with the two usual

conditions:

1) the instrument must be correlated with the endogenous variable, that is

(

PeerCourse,Z

)

≠0

Cov ;

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12

reasons other than its influence on the formation of peer groups. It is required that the

instrument is exogenous, that is Cov

( )

Z,ε =0;

We believe that our second definition of peer group (Peer First Degree) has these

characteristics. Peer First Degree is based on the classes attended by students in the first years

of their First Level Degree course. Students in our sample were already enrolled at the

University of Calabria for their First Level Degree. As a result of the high number of students

enrolled in the First Level Degree course in Business Administration (about 600 students), they

were assigned to three different teaching classes (Class 1, 2 and 3) for each compulsory course

in the first two years on the alphabetic basis of the initial letter of their surnames. Students were

required to attend lectures in their designated teaching classes and, moreover, it was in the

student’s interest to respect this arrangement, because final exams were laid out autonomously

by the lecturers teaching each class (notwithstanding common programmes). For each year, we

consider as peers all the students attending the same compulsory course as part of the same

assigned classes13 and calculate peer group quality as the average ability of these students (using

our three measures of ability).

This definition of peer group, Peer First Degree, is likely to determine the quality of

peers on the Second Level Degree course since the repeated interactions taking place among

students in these classes are relevant to the defining of their peer group composition: students

typically tend to associate, make friends, form stable groups and continue studying over the

following years with people who attend the same classes, even during their Second Level

Degree course.14 Therefore, Cov

(

PeerCourse,PeerFirstDegree

)

≠0. Obviously, this aspect can

be empirically tested and, as we show below, the coefficient of the instrumental variable Peer

First Degree in the first-stage regressions is always highly significant and the F-test used to

verify that our instrument is not weak is highly supportive.

With regards to exogeneity, the Peer First Degree variable is likely to be exogenous

given the random assigning to classes according to alphabetical order and the stringent

requirements for students to attend these classes.

Moreover, belonging to a given teaching classes should not determine a student’s

academic performance (except through its influence on the composition of peer groups), since,

except for instructors’ quality characteristics, for which we control, resources devoted to

different teaching classes are the same and the same institutional structure was valid over the

two years. For these reasons, we are confident that Cov

(

PeerFirstDegree

)

=0

First of all, in order to check that our instrument is not “weak”, we have tested whether

the instrument in the first stage regression is significantly different from zero. In the first-stage

regression in which the endogenous variable, Peer Course, is regressed on the instrument, Peer

13

The average number of peers according to this definition is 40.83.

14

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13

First Class, and all other exogenous variables, the F-statistics, for the test of whether the

instrument coefficient is equal to zero, are always well above the threshold value of 10

suggested by Stock and Watson (2003) (F-statistics range from 33 to 140 according to different

measures of abilities used).

As a further check that the instrument is not weak, as suggested by Angrist and Krueger

(1999), in Table 3, we report results from three different estimates of the reduced-form equation

in which the dependent variable is regressed on all the exogenous variables and on the

instrumental variable, Peer First Degree: in column 1, we use AbilityHS as a measure of peer

ability, in column 2, we use AbilityFirst and, finally, in column 3, we measure ability using the

comprehensive index Ability. Peer First Degree is highly significant in all the specifications,

implying both that our instrumental variable is a strong determinant of peer group quality and

that the peer group influences a student’s academic performance. Instructors’ seniority and

research productivity (measured respectively as the number of years an instructor has worked in

the university system in a permanent position and as the number of published articles in referred

[image:14.595.88.449.432.692.2]

journals per year) are not statistically significant.

Table 3. Reduced form equation estimates of academic achievement. Dependent variable: Average Grade in Second Level Degree course exams

Explanatory Variables 1 2 3

AbilityFirst 0.549***

[0.049]

0.548*** [0.054]

AbilityHS 0.079*

[0.039]

0.084* [0.042]

Ability 0.566***

[0.057]

Female 0.002

[0.048]

-0.006 [0.040

-0.111 [0.061]

Lyceum 0.001

[0.048]

0.004 [0.104]

Average Course Grade 0.360***

[0.028]

0.360*** [0.028]

0.354*** [0.028]

Peer First Degree (AbilityHS) 0.104***

[0.026]

Peer First Degree (AbilityFirst) 0.053**

[0.018]

Peer First Degree (Ability) 0.146***

[0.018]

Instructors’ seniority 0.087

[0.093]

0.267** [0.077]

0.034 [0.045]

Instructors’ publications 0.072

[0.087]

0.229** [0.058]

0.047 [0.040]

Constant -0.136

[0.091]

-0.138 [0.093]

-0.103 [0.125]

Adjusted R2 0.572 0.568 0.534

Observations 212 212 212

Notes: Dummies are included in all regressions for province of residence. Standard errors, corrected for heteroskedasticity and adjusted for potential clustering at teaching class level, are reported in brackets. The symbols ***, **, * indicate that coefficients are statistically significant, respectively, at 1, 5, and 10 percent levels.

Two-Stage Least Squares

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14

academic performance using the Peer First Degree variable as an instrument for peer group

quality.

Before using an instrumental variable estimator, since OLS would be more efficient

than IV under the hypothesis that OLS are consistent, one should check whether it is necessary

to use IV at all. In order to verify this aspect, we run the Durbin-Wu-Hausman test to verify the

endogeneity of Peer Course in OLS. We take the residuals from the first stage regression and

insert them, as explanatory variables, into an “augmented” structural equation. In many of our

specifications, this variable is significantly different from zero (with the exception of the ability

measure “Ability First”) showing that OLS is not consistent and suggesting the use of IV to

address the problem of endogeneity.

Two-Stage Least Squares Estimations results are shown in Table 4. As above, the three

columns use AbilityHS, AbilityFirst and Ability respectively as a measure of peer ability.

Panel B of Table 4 shows the results from First Stage regressions for the different peer

ability measures. In all the specifications, it emerges that Peer First Degree strongly determines

the quality of the peer group as measured by Peer Course. Moreover, peer group quality is also

influenced by a student’s own individual abilities.

Panel A shows Two Stage Least Squares estimations. Peer Course coefficients are

always positive and highly significant, regardless of how ability is measured. In column 1,

controlling for Instructors’ publications and seniority, if peer group quality (measured by

AbilityHS) increases by one standard deviation then a student’s performance improves by

0.24. This coefficient is significant at 10 percent level. In columns 2 and 3, using AbilityFirst

and Ability respectively, an increase of one standard deviation in peer quality leads to an

improvement in student performance of 0.09 and 0.19 respectively (significant at 5 and 1

percent levels).

In general, the IV coefficients are higher than the OLS coefficients. This suggests that

measurement errors in the quality of peer group – which may bias our coefficient of interest

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[image:16.595.82.465.83.611.2]

15 Table 4. IV regressions of student’s academic performance

Dependent variable: Average Grade in Second Level Degree course exams

Explanatory Variables 1 2 3 Panel A: Two-Stage Least Squares

AbilityFirst 0.485*** [0.083] 0.530*** [0.051]

AbilityHS 0.106

[0.059]

0.089* [0.042]

Ability 0.541***

[0.055]

Female -0.051

[0.034]

-0.016 [0.050]

-0.123 [0.072]

Average Course Grade 0.306***

[0.033]

0.349*** [0.031]

0.317*** [0.029]

Lyceum 0.022

[0.102]

0.004 [0.103]

Peer Course (AbilityHS) 0.237*

[0.099]

Peer Course (AbilityFirst) 0.089**

[0.027]

Peer Course (Ability) 0.188***

[0.027]

Instructors’ publications 0.124

[0.135]

0.222*** [0.052]

0.163** [0.060]

Instructors’ seniority 0.117

[0.158]

0.240** [0.068]

0.145* [0.067]

Constant -0.146

[0.079]

-0.130 [0.087]

-0.099 [0.101]

Panel B: First Stage Regressions

AbilityFirst 0.268***

[0.700]

0.202*** [0.051]

AbilityHS -0.112

[0.075]

-0.058 [0.053]

Ability 0.133***

[0.047] .

Female 0.224

[0.123]

0.116 [0.086]

0.062 [0.096]

Average Course Grade 0.231***

[0.053]

0.129*** [0.037]

0.194*** [0.043]

Lyceum -0.303

[0.318]

-0.001 [0.081]

Peer First Degree (AbilityHS) 0.436***

[0.075]

Peer First Degree (AbilityFirst) 0.600***

[0.046]

Peer First Degree (Ability) 0.775***

[0.047]

Instructors’ publications -0.220

[0.310]

0.080 [0.192]

-0.616** [0.250]

Instructors’ seniority -0.126

[0.325]

0.303 [0.196]

-0.591** [0.267]

Adjusted R2 0.367 0.679 0.611

Observations 212 212 212

Notes: Panel A reports the Two-Stage Least Squares estimates, instrumenting Peer Course using Peer First Degree. Panel B reports the corresponding first stage. Dummies are included in all regressions for province of residence. Standard errors, corrected for heteroskedasticity and adjusted for potential clustering at teaching class level, are reported in brackets. The symbols ***, **, * indicate that coefficients are statistically significant, respectively, at 1, 5, and 10 percent levels.

Evaluating Peer effects for individuals who study together

Students belonging to the same class tend to study and revise the subject together, so generating

important externalities. However, this kind of relationship does not develop between all the

members of a class, since, even though attending courses together, some students may not

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16

(called Peer Exam) based on this type of interaction, which we believe particularly relevant, we

consider as members of the same group students who sit an exam on the same date. Anecdotal

evidence suggests that students who study together tend to take exams together.

In each academic year, students in our sample have 7 different dates available to take a

given exam. For each student, we are able calculate how many times he/she meets any other

students at exams or, more precisely, how many times they passed an exam on the same date.15

Students who meet more often at exams are presumably part of the same group. Therefore, we

calculate the ability of the peer group as a weighted average of “matched” students’ abilities

(with the three measures: AbilityHS, AbilityFirst and Ability), using the number of matches at

exams as weights:

=

= i

n

j

j ij i

i m A

M PeerExam

1 1

where Aj is the ability of student j, mij is the number of times student i met student j at exams,

i

n is the number of students met by i, and

=

= i

n

j ij i m M

1

is the total number of matches of i.

This measure of peer group ability weights the ability of each member of the peer group

according to the number of exams taken together: students who are found to have often sat

exams together are given a higher weight, while those who match less frequently are weighted

less.16 A similar strategy to building a peer group is followed by Bayer et al. (2007)17 and De

Giorgi, Pellizzari and Redaelli (2006).

Columns 1, 2 and 3 in Table 5 use Peer Exam, calculated using our alternative measures

of ability, and instrument this variable (which we strongly suspect to be endogenous), again

using Peer First Degree. The Durbin-Wu-Hausman test shows that OLS would not be

consistent (for example, using Ability, the t-statistics of residuals in the augmented structural

regression is equal to 3.12) and support the use of IV to address the problem of endogeneity.

Through this new definition of peer group, our previous results with regards the

relevance of peer effects are confirmed. In fact, the results show that: (a) Peer First Degree

determines the formation of a peer group (as shown by the high significance of the relative

coefficient in first stage regressions and by the test for weak instruments for which F-statistics

takes on values from 26 to 170) and that (b) peer group quality is an important determinant of a

student’s academic performance (regardless of how abilities are measured). In column 1, we

show that if Peer Exam measured using AbilityHS increases by one standard deviation, then a

15

Unfortunately, we have data on passed exams only, as no information is available regards failed exams.

16

We also experimented with a measure of peer group which excludes from the peer group all students sitting together only once or twice (because this meetings could be due to pure chance). Results are similar to those reported.

17

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17

student’s academic performance improves by 0.26 (the coefficient is significant at 5 percent

level). Analogous results are obtained if we use alternative measures of peer group abilities. For

example, using Ability, we find that an increase of one standard deviation in the peer group

quality leads to an improvement of 0.28 in the student’s academic performance (significant at a

1 percent level).

These coefficients are slightly higher compared to those obtained by considering all

students attending courses together as peer groups, implying that students’ performance is more

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[image:19.595.81.493.91.611.2]

18 Table 5. IV regressions of student’s academic performance

Dependent variable: Average Grade in Second Level Degree course exams

Explanatory Variables 1 2 3 Panel A: Two-Stage Least Squares

AbilityFirst

0.520*** [0.062] 0.534*** [0.056]

AbilityHS 0.051

[0.057]

0.069 [0.051]

Ability 0.494***

[0.075]

Female 0.003

[0.049]

0.002 [0.044]

-0.079 [0.078]

Average Course Grade 0.310***

[0.037]

0.360*** [0.031]

0.313*** [0.036]

Lyceum 0.021

[0.101]

0.004 [0.111]

Peer Exam (AbilityHS) 0.263**

[0.098]

Peer Exam (AbilityFirst) 0.097**

[0.034]

Peer Exam (Ability) 0.282***

[0.045]

Instructors’ publications 0.191

[0.095] 0.248*** [0.048] 0.192*** [0.025] Instructors’ seniority 0.185 [0.113] 0.271*** [0.067] 0.165*** [0.027]

Panel B: First Stage Regressions

AbilityFirst 0.112

[0.072]

0.139*** [0.068]

AbilityHS 0.106

[0.076]

0.153 [0.071]

Ability 0.256***

[0.059]

Female -0.002

[0.125]

-0.080 [0.116]

-0.115 [0.121]

Average Course Grade 0.191***

[0.054]

0.002 [0.050]

0.145** [0.054]

Lyceum -0.077

[0.119]

0.020 [0.058]

Peer First Degree (AbilityHS) 0.394***

[0.077]

Peer First Degree (AbilityFirst) 0.600***

[0.046]

Peer First Degree (Ability) 0.518***

[0.080]

Instructors’ publications -0.453

[0.316]

-0.199 [0.259]

-0.516 [0.314]

Instructors’ seniority -0.374

[0.331]

-0.038 [0.264]

-0.464 [0.335]

Adjusted R2 0.268 0.373 0.377

Observations 212 212 212

Notes: Panel A reports the Two-Stage Least Squares estimates, instrumenting Peer Course using Peer First Degree. Panel B reports the corresponding first stage. Dummies are included in all regressions for province of residence. Standard errors, corrected for heteroskedasticity and adjusted for potential clustering at teaching class level, are reported in brackets. The symbols ***, **, * indicate that coefficients are statistically significant, respectively, at 1, 5, and 10 percent levels.

5. Concluding remarks

A large amount of empirical literature shows that peer group quality has important effects on a

student’s performance and, more in general, on an individual’s results. While, for primary and

secondary education, there is considerable literature analyzing the effects of classmates’ quality

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19

effects emerging among roommates and little is known about the effects produced on college

students by different teaching environments.

Thanks to a rich administrative dataset, we are able to build different definitions of the peer

group, mainly based on students attending classes together, interacting in study activity and

sitting their exams in the same session. This allows us to investigate peer group effects which

occur among classmates through mechanisms which rely on the fact that classmates contribute

to the shaping of the educational environment.

In addition, most research on peer group effects in education is focussed on the US,

whereas very few studies examine European schools or universities. To our knowledge, this

paper is the first attempt to evaluate peer effects in an Italian university.18 Moreover, whereas

many papers study highly selective universities with rather homogeneous groups (see Sacerdote,

2001), the students we consider are not sorted through a selection process and are highly

heterogeneous in terms of abilities. This factor, which widens variability, is likely to increase

the relevance of peer effects.

We regress the student’s Average Grade in the Second Level Degree course on his/her

own predetermined characteristics and abilities and on his/her peers’ abilities. We use a variety

of definitions of peer group – based on the courses taken together, on classes attended during

the First Level Degree course, on the dates of exams– and use different measures of abilities

(Final High School Grade, Average First Level Degree Grade, type of High School etc.). It is

likely that the peer group, defined both in terms of classes attended and of exams taken together,

will encompass the relevant interactions among students.

In order to overcome the reflection problem, one of the main econometric problems that

affects estimates of peer effects, we use predetermined variables for abilities, but do not attempt

to distinguish the channels through which peer group influences a student’s performance. From

a policy point of view, this is not particularly detrimental.

The second econometric problem in estimating peer effects is the endogeneity of the

peer group, in that individuals tend to choose people with whom to associate. In order to solve

this issue, we estimate a model with Two-Stage Least Squares, using, as an instrument for peer

group, the teaching classes to which students were assigned within compulsory courses during

their First Level Degree.

Our results show very clearly that peer effects are positive and substantial. Being part

of a group with higher abilities considerably improves a student’s academic performance.

Results are robust to different definitions of a peer group and different measures of ability used.

Peer group effects emerging from our analysis are, in most of the specifications, larger

in magnitude than those shown in other studies (Sacerdote, 2001; Zimmerman, 2003). This

18

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20

could be due to the fact that our measure of peer group quality includes interactions among

students – based on attending the same classes, sharing the same educational environment and

studying together – which are likely to be greater than those deriving from sharing the same

accommodation . In fact, people sharing the same room may have limited interaction due to the

fact that they specialise in different areas and have different interests. On the other hand,

students attending the same courses or working together establish relationships that are crucial

in determining effective learning processes.

According to our results, student quality is an important input in tertiary education

implying that attracting high quality students helps colleges and universities to improve their

students’ performance. Positive effects produced by high quality peers are consistent both with

the highly selective policies adopted by many US universities and the high fees that students are

willing to pay to be admitted to these universities.

Peer effects by definition imply positive or negative externalities which lead individual

choices to be different from optimal social choices. If we realistically assume – following the

analysis of Costrell (1994) and Kremer, Miguel and Thorntorn (2007) – that student ability is

not only due to genetic factors, but is also the outcome of student effort during his/her

educational career, our results suggest that high achieving students should be subsidized

(through scholarships and grants) for the positive externalities they produce on other students.

On the other hand, students who perform badly may be encouraged to increase their sub-optimal

level of effort by tuition fees which are inversely related to their academic performance

(Garibaldi et al., 2007).

References

Ammermueller, A. and Pischke, J., (2006), “Peer Effects in European Primary Schools. Evidence from PIRLS”, NBER Working Paper no. 12180.

Angrist, J. and Krueger A. (1999), “Empirical Strategies in Labor Economics”, Handbook of Labour Economics, pp. 1277-1366.

Angrist, J. D. and K. Lang, (2004), “Does School Integration Generate Peer Effects? Evidence from Boston's Metco Program”, American Economic Review, 94 (5), pp. 1613-1634. Arcidiacono, P. and S. Nicholson, (2005), “Peer Effects in Medical School”, Journal of Public

Economics, 89, pp. 327-350.

Arcidiacono, P., Foster, G., Goodpaster, N., Kinsler, J. (2005), “Estimating Spillovers in the Classroom with Panel Data”, mimeo Duke University.

Bayer, P., Hjalmarsson, R., Pozen, D. (2007), “Building Criminal Capital behind Bars: Peer Effects in Juvenile Corrections”, NBER Working Paper no. 12932.

Betts, J., and Morell, D., (1999), “The Determinants of Undergraduate GPA: The Relative Importance of Family Background, High School Resources, and Peer Group Effects,”

Journal of Human Resources, pp. 268–293.

Case, A., and Katz, L., (1991), “The Company You Keep: The Effect of Family and Neighborhood on Disadvantaged Youths,” NBER Working Paper No. 3705.

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21

Costrell, R., (1994), “A Simple Model of Educational Standards.” American Economic Review,

84 (4), pp. 956–71.

De Giorgi, G., Pellizzari, M., Redaelli, S., (2006), “Be as careful of the books you read as of the company you keep. Evidence on peer effects in educational choices”, mimeo.

Ding W. and Lehrer S. (2006), “Do Peers Affect Student Achievement in China’s Secondary chool?” NBER Working Paper No. 12305.

Epple, D. and R. E. Romano, (1998), “Competition between private and public schools, vouchers, and peer-group effects”, American Economic Review, 88 (1), pp. 33-62.

Evans, W, Oates, W. and Schwab, R. (1992), “Measuring Peer Group Effects: A Study of Teenage Behavior”, Journal of Political Economy, 5, pp. 966-991.

Foster, G., (2006), “It's not Your Peers, And It's Not Your Friends: Some Progress Toward Understanding the Educational Peer Effect Mechanism”, Journal of Public Economics, pp. 1455-75.

Garibaldi, P., Giavazzi, F., Ichino, A., Rettore, E., 2007, “College Cost and Time to Complete a Degree: Evidence from Tuition Discontinuities”, NBER Working Paper, N. 12863. Hanushek, E. A., J. F. Kain, J. M. Markman, and S. G. Rivkin, (2003), “Does peer ability affect

student achievement?”, Journal of Applied Econometrics, 18 (5), 527-544.

Hoxby, C., (2000), “Peer effects in the classroom: Learning from gender and race variation”,

NBER Working Paper 7867.

Kremer, M., Miguel, E. and Thornton, R. (2007), “Incentives to Learn”, mimeo, Harvard University.

Lazear, E., (2001), “Educational Production”, Quarterly Journal of Economics, 3, pp. 777-803. Manski, C., (1993), “Identification of Endogenous Social Effects: The Reflection Problem”

Review of Economic Studies, 60, pp. 531–542.

Moulton, B.R. (1990), “An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Units”, The Review of Economics and Statistics, pp. 334-338.

Sacerdote, B., (2001), “Peer Effects with Random Assignment: Results for Dartmouth Roommates”, Quarterly Journal of Economics, 681-704.

Sawkins, J., (2002), “Examination Performance in Scottish Secondary Schools: An Ordered Logit Approach”, Applied Economics, 34, pp. 2031-41.

Stock, J. and M. Watson, (2003), Introduction to Econometrics, Pearson Education Inc.

Vandenberghe V. (2002), “Evaluating the magnitude and the stakes of peer effects analysing science and math achievement across OECD”, Applied Economics, 34, 1283-1290. Zimmer, R. W. and E. Toma, (2000), “Peer effects in private and public schools across

countries”, Journal of Policy Analysis and Management, 19 (1), 75-92.

Figure

Table 1. Descriptive statistics for the sample of students enrolled on the Second Level Degree course in Business Administration
Table 2. OLS regression estimates for academic achievement.  Dependent variable: Average Grade in Second Level Degree course exams
Table 3. Reduced form equation estimates  of academic achievement.  Dependent variable: Average Grade in Second Level Degree course exams
Table 4. IV regressions of student’s academic performance
+2

References

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